For spatial discretization the implementation uses linear finite elements and for time discretization we use the BDF3 method as presented in the former chapter. As the domain we use the two-dimensional unit disk, and meshes that are generated via DistMesh [1]}. We will show results for different mesh sizes and different time step sizes. We choose the inhomogeneities, \(f_1^\Omega , f_2^\Omega , f_1^\Gamma \)  and \(f_2^\Gamma \) , such that the solution of (REF )–(REF ) respectively (REF )–(REF ) is \((u, w)= (e^{-t}xy,e^{-t}xy)\) .
For the nonlinear case we consider the Cahn–Hilliard equation with double-well potential, both in the bulk and on the surface, therefore we choose the nonlinearity \(F(u)=u^3-u\) .
